Plug this in your calculator If f(x) = 1/(1 - x), g(x) = x/(1 - x), and h(x) = 1/(1 + x), then f[h(x)] =?

Question

did anyone get

(1+x)/x

Answer 1

Yep, (1+x)/x

Answer 2

You can ignore g(x) for this problem...

Simply plug h(x) into the equation for f(x)

f(x) = 1/(1 - x)
h(x) = 1/(1 + x)

f(h(x)) = 1/(1 - [1/(1+x)]

Let's work on that denominator:
1 - 1/(1+x)

Get a common denominator of (1+x):
[ (1+x) - 1 ] / (1 + x)

Simplify:
x / (1 + x )

But remember that was the denominator in 1 / ?

So the final answer is the reciprocal:
(1 + x ) / x

Yes, you got the right answer!

Answer 3

yes